If I remember correctly, the SST-6 has a rubber sole for the non-slide shoe. If you are having trouble with traction on this shoe, you may need to wipe the shoe every now and then. I know many people who, as part of their pre-shot routine, wipe the sole of their non-slide shoe before every shot. Perhaps before practice, take a damp cloth to the sole to get rid of any residual dust.
I used to have issues when I kept powder, rosin and easy slide in the same compartment as my shoes. Now all those things are kept in ziplok bags and I have fewer problems.
If you want to wear an athletic type shoe on the non-slide foot, then make sure they feel comfortable when worn with your bowling shoe. Things like sole heights and slope can affect they comfort and feel during bowling. Bowling shoes have a very small slope from heal to toe where most athletic shoes have a higher slope due to extra cushioning in the heel. "Minimalist" athletic shoes are a newer shoe designed with a zero, or close to it, slope from heal to toe. Gives the effect of being back on your heals the first time you wear them. These may be closer to the "feel" of bowling shoes. Then again, whatever shoe you use, you will probably get used to them quickly.
Irregardless of the shoe you choose, do make sure they are non-marking. Even after sliding, your right foot becomes part of a sweeping balance leg behind you and can leave marks on the approach.
I am not a pro-bowler, but I do play one on BallReviews.com